Density Models

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Description

SECR can fit an inhomogeneous Poisson model to describe the distribution of animals. This may be viewed as a surface of expected density across the study area.

The log likelihood is evaluated in secr.fit by summing values at points on a ‘habitat mask’. Each point in a habitat mask represents a grid cell of potentially occupied habitat (their combined area may be almost any shape and may include disjunct patches).

The density model may take one of two forms: a user-provided R function or a linear model on the link scale (see the link argument of secr.fit; the default link for density is ‘log’). User-provided functions are described in the accompanying vignette secr-densitysurfaces.pdf. Here we focus on linear models.

The full design matrix for density (D) has one row for each point in the mask. The design matrix has one column for the intercept (constant) term and one for each predictor. Predictors may be based on Cartesian coordinates (e.g. ‘x’ for an east-west trend), a continuous habitat variable (e.g. vegetation cover) or a categorical (factor) habitat variable. Predictors must be known for all points in the mask (non-habitat excluded). The variables ‘x’, ‘y’, ‘x2’, ‘y2’, ‘xy’, ‘session’, ‘Session’ and ‘g’ are provided automatically. Other covariates should be named columns in the ‘covariates’ attribute of the habitat mask.

Variable Description Data source
x x-coordinate automatic
y y-coordinate automatic
x2 x-coordinate^2 automatic
y2 y-coordinate^2 automatic
xy x-coordinate * y-coordinate automatic
session session factor automatic
Session session number 0:(R-1) automatic
g group factor automatic
[user] mask covariate covariates(mask) as named in formula

The submodel for density (D) is a named component of the list used in the model argument of secr.fit. It is expressed in R formula notation by appending terms to \~.

Density surfaces resulting from the fitting of SECR models are manipulated in secr as objects of class ‘Dsurface’. See the vignette secr-densitysurfaces.pdf for details and examples, including functions for prediction and plotting.

Note

Note that no density model is fitted when secr.fit is called with CL = TRUE.

References

Borchers, D. L. and Efford, M. G. (2008) Spatially explicit maximum likelihood methods for capture–recapture studies. Biometrics 64, 377–385.

See Also

secr models, secr detection models, secr.fit, Dsurface, predictDsurface, plot.Dsurface

Examples

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D = ~ 1      ## constant density (homogeneous Poisson)
D = ~ x      ## east-west trend
D = ~ cover  ## requires 'cover' as a mask covariate

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